Symbolab

I've just had a look at a website called Symbolab that offers a many tools for the mathematics student and even the chemistry student. I tested it out with the following rather difficult integral:

I was impressed with the step-by-step solution provided for the problem. It was quite thorough. It seems to be largely free, although there is a modestly priced paid option, and there is both an Android and iOS app that I'll download and test out. It seems a worthy competitor to WolframAlpha that doesn't offer free, step-by-step solutions on its website or apps.

I was made aware of the site thanks to Richard Byrne's tweet:

https://twitter.com/rmbyrne/status/775696157171253248

I used to follow this guy but hadn't been doing so over the past year since I retired from full-time teaching. However, I reconnected yesterday and the reconnection is already paying benefits. I've opened a free account using my Facebook login.

UPDATE: having now downloaded the Android app, I've found that the step-by-step solutions are only available with a one-off payment of $9.99 (US dollars presumably) which is a lot more than WolframAlpha is asking. The iOS app is the same except that it wants $10.99. Consequently, I've uninstalled both the Android and iOS apps and will simply use the desktop version while it still provides the steps for free. The web version is still limited in various ways. For example, the full range of practice questions on various topics is only available via a subscription. 

Creating Online Courses and Classes

moodlecloud offers a free service along with paid plans

Despite my retirement from active teaching, I remain interested in education and am engaged in intermittent mathematics tutoring. I'm always on the lookout for ways to extend the tutoring session beyond the hour or so that I spend face-to-face with my student. To this end, I've made use of moodlecloud that provides a free service as well as paid options. Having so far only one student at any given time, I've found that the free service is quite adequate. Even though only 250 MB of storage is available, I've only used a small fraction.

The free service is adequate for those with a small number of students

Of course, it means that you can't upload large video files but you can link to them and that's enough. The free option is an excellent choice for people who work with only a small number of students.

When I was teaching full-time, I used the school-based Moodle installation most of the time but I did dabble with Edmodo and I still have an account. I recently archived my old courses and even posted to the Mathematics Forum. I may begin to experiment with it again. The site has an app that enables access via smartphone or tablet, so that's useful.

My Edmodo profile

I've also been experimenting with a site called Versal, that amongst other things offers an excellent tool for rendering mathematical expressions.

An example of the rendering of mathematical expressions

Of course, there's a hundreds of similar sites out there but these are three that I am using or have used, and they are all free. While writing this I was reminded of an excellent educational blog that I used to reference but haven't done so since leaving teaching. Here is the link. 

This site offers excellent reviews of educational resources

WolframAlpha

For the PRO version of the desktop WolframAlpha, there is a charge $6.99 per month (on a month by month basis) and I'm not sure whether the quote is for United States or Australian dollars. However, the mobile version of WolframAlpha seems to offer some, perhaps all, of the features of the desktop PRO version for a one-off cost of A$4.99. Whether it's totally equivalent to the PRO version or not I'm not sure but it certainly provides the step-by-step solutions that the former offers.

Anyway, I've made the mobile purchase and am experimenting with it. I tried the step-by-step solution to integrating ln(x^2+1) and it's displayed in the mobile app but I can't see how to copy it. Screenshots can of course be taken and this is what I've done below. The result is OK I guess.

Sway

Another spinoff of installing Windows 10 on VirtualBox was the discovery of Microsoft's Sway, described by Wikipedia as follows:

Office Sway is a presentation program and is part of the Microsoft Office family of products. Generally released by Microsoft in August 2015, Sway allows users who have a Microsoft account to combine text and media to create a presentable website. Users can pull content locally from the device in use, or from internet sources such as Bing, Facebook, OneDrive, and YouTube. Sways are stored on Microsoft's servers and are tied to the user's Microsoft account. They can be viewed and edited from any web browser with a web app available in Office Online. They can also be accessed using apps for Windows 10 and iOS. Additional apps are currently in development for Android and Windows Phone.

Sway is only available within Windows or iOS, so I have installed it on my iPad after discovering it on my Windows 10 installation and wondering what it was all about. Here is my first effort at creating a Sway presentation:

From Evernote to OneNote

With Evernote's decision to limit free accounts to access from only two devices, I decided it was time to abandon a platform that I'd been using almost from its inception. I'm sure I'll have lots of company. There's something very annoying about crippling a service that was formerly provided for free and increasing the price of the paid service options. 

I opted for OneNote over Google Keep (although I plan to test out the latter in the near future) and then investigated whether it was possible to migrate notes from Evernote to the OneNote. It turns out that is possible but the tool provided by Microsoft only works with Windows. I discovered that it was possible to run Windows 10 with no product key under VirtualBox, so I downloaded and installed it. 

I then downloaded Evernote for Windows, synched all my notes, downloaded the migration tool and moved all my notebooks, notes and tags across to OneNote. It turns out that I had 2001 notes. The migration is proceeding as I write and the whole process has proved relatively painless, with the major difficulty proving to be the download of the 4Gb ISO file. The downloaded failed two times but succeeded on the third attempt.

So as well as successively moving all my Evernote notes to OneNote, I now have an installation of Windows 10 on VirtualBox as well as the latest version of Ubuntu.

Precariat

When the Bilderberg Group listed precariat as one of their ten items for discussion at their 2016 meeting, many outsiders (and nearly everybody on the planet is an outsider) would have reached for their electronic or physical dictionaries to look up the meaning of this word. I know I did.

Well it turns out that precariat is a portmanteau formed by merging precarious with proletariat. Here is an excerpt from the Wikipedia article:

In sociology and economics, the precariat is a social class formed by people suffering from precarity, which is a condition of existence without predictability or security, affecting material or psychological welfare. Unlike the proletariat class of industrial workers in the 20th century who lacked their own means of production and hence sold their labour to live, members of the Precariat are only partially involved in labour and must undertake extensive "unremunerated activities that are essential if they are to retain access to jobs and to decent earnings". Specifically, it is the condition of lack of job security, including intermittent employment or underemployment and the resultant precarious existence. The emergence of this class has been ascribed to the entrenchment of neoliberal capitalism.

 A recent article (June 8th 2016) in QUARTZ included this description:

The "precariat" is a term popularised by British economist Guy Standing, describing a growing class of people who feel insecure in their jobs, communities, and life in general. They are… 

… the perpetual part-timers, the minimum-wagers, the temporary foreign workers, the grey-market domestics paid in cash … the techno-impoverished whose piecemeal work has no office and no end, the seniors who struggle with dwindling benefits, the indigenous people who are kept outside, the single mothers without support, the cash labourers who have no savings, the generation for whom a pension and a retirement is neither available nor desired. 

This marginalised group—“alienated, anomic, anxious, and angry,” according to Standing—is fuelling the rise of populist politicians like Donald Trump in the US and similar rabble rousers in Europe and beyond. (Discussing this group alongside the middle class, which isn’t doing great either, is telling.) The resulting turmoil in politics, markets, and economics is a factor in nearly all of the Bilderberg meeting’s other agenda items.

The word isn't recognised by Blogger's spell checker but it is certain to become better known now that the global elite are discussing it and, by whatever name this category of people may be called, it is growing rapidly in size. Here is Amazon's review of Guy Standing's book:

Described by Noam Chomsky as 'a very important book', Guy Standing's The Precariat has achieved cult status as the first account of this emerging class of people, facing lives of insecurity, moving in and out of jobs that give little meaning to their lives. 

Guy Standing warns that the rapid growth of the precariat is producing instabilities in society. It is a dangerous class because it is internally divided, leading to the villainisation of migrants and other vulnerable groups. And, lacking agency, its members may be susceptible to the siren calls of political extremism. He argues for a new politics, in which redistribution and income security are reconfigured and in which the fears and aspirations of the precariat are made central to a progressive strategy. 

Since first publication of this book in 2011, the precariat has become an ever more significant global phenomenon, highly visible in the Occupy movement and in protest movements around the world. 

In a new preface Guy Standing discusses such developments - are they indicative of the emergence of a new collective spirit, or do they simply reveal the growing size and growing anger of this new class?

Native German Words That English Uses

Today I came across a German word, Gegenschein, that I'd not heard of before. It means "a faint, elliptical patch of light in the night sky that appears opposite the sun, being a reflection of sunlight by meteoric material in space". In German, the word Gegenschein means counterglow (gegen meaning against and Schein means light). It reminded me of other words rather more common German words that have found their way into English unchanged. Here are some that I remember:

• Schadenfreude: delight in another's misfortune (Schaden means harm and Freude means joy)
• Weltanschauung: a comprehensive view or personal philosophy of human life and the universe (Weltan means world and Anschauung means view)
• Zugzwang: a position in which one player can move only with loss or severe disadvantage (Zug means pull or tug, Zwang means force, compulsion)
• Weltschmerz: sadness or melancholy at the evils of the world; world-weariness (literally world pain)
• Zeitgeist: the spirit, attitude, or general outlook of a specific time or period, esp as it is reflected in literature, philosophy, etc. (Zeit means time and Geist means spirit)
• Wanderlust: a great desire to travel and rove about (literally wander desire)
• Ersatz: used as an adjective meaning "made in imitation of some natural or genuine product; artificial" from ersetzen to substitute. It should be noted that the German word has a neutral connotation, e.g. Ersatzrad simply means "spare wheel" (not an inferior one).
• Gestalt: a perceptual pattern or structure possessing qualities as a whole that cannot be described merely as a sum of its parts (from Old High German stellen to shape).
• Leitmotif: in music, a recurring short melodic phrase or theme used, especially in Wagnerian music dramas, to suggest a character, thing, etc.; an often repeated word, phrase, image, or theme in a literary work (from leitmotiv leading motif).

That's probably enough for now, although there are many more.